A universal Hamiltonian for motion and merging of Dirac points in a two-dimensional crystal
By Gilles Montambaux, F. Piéchon, J. Fuchs, M. Goerbig. 2009
155 citations recorded by the source corpus.
AbstractWe propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac cones from an insulating phase with a gap. We calculate the density of states and the specific heat. The spectrum in a magnetic field B is related to the resolution of a Schrödinger equation in a double well potential. The Landau levels obey the general scaling law epsilonn ∝B2/3 fn(Δ/B2/3), and they evolve continuously from a $\sqrt{n B}$ to a linear (n+1/2)B dependence, with a [(n+1/2)B]2/3 dependence at the transition. The spectrum in the vicinity of the topological transition is very well described by a semiclassical quantization rule. This model describes continuously the coupling between valleys associated with the two Dirac points, when approaching the transition. It is applied to the tight-binding model of graphene and its generalization when one hopping parameter is varied. It remarkably reproduces the low field part of the Rammal-Hofstadter spectrum for the honeycomb lattice.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/564a5d616b1b0595faebe592a3c828a8b331cdcf
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Electronic properties of graphene in a strong magnetic field (2010, background): “…the vicinity of the transition, one may expand the Hamiltonian (59) around the merging point M ′′ (Montambaux et al., 2009a,b), and one finds6 HMq = ( 0 ∆ + ~ 2q2x 2m∗ − i~cqy ∆+ ~ 2q2x 2m∗ + i~cqy 0 ) , (64) in terms of the mass m∗ = 2~2/3ta2 and the velocity c = 3ta/~ (Montambaux et al., 2009b).”